Functions was the final strand to be introduced in phase 3 of the new Project Maths Course. This topic provides an essential link between Algebra and Number and introduces the students to applications of calculus in the real world. Use of differentiation to find the slope of a tangent to a curve at a specified point is introduced. This is then extended to the study of increasing and decreasing functions. Functions and Differentiation are used in real life to help us understand rates of increase and decrease. For example, students will solve problems involving the maximum speed reached by a car and the highest point reached by a firework or rocket. Finally, the concept of numerical integration is introduced through the use of the ‘Trapezoidal Rule’ to find areas under specific curves.
Having completed this course students will be able to:
- Basic Differentiation of functions
- The rules of differentiation (product rule, quotient rule, chain rule)
- Determine the local maxima and local minima turning points of a curve
- Understand rate of change of distance
- Use slope to determine the nature of a function
- How to use the Trapezoidal Rule to find area
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Strand 5 Ordinary Level Functions and Calculus
Modules List( 3 )
PROJECT MATHS STRAND 5 ORDINARY LEVEL: FUNCTIONS A...
Learn more about functions.
- Plotting quadratic graphs from table of values
- Plotting cubic graphs from table of values
- Plotting reciprocal graphs from table of values
- Plotting exponential graphs from table of values
- Matching equations and sketches
- Matching functions and graphs – quadratic / exponential
- Translation of functions using f(x-a)
- Translating of functions using f(x)+a
- Stretching functions in x direction
- Stretching functions in y direction
- The Discriminant
Module 2: Calculus - Differentiation
Learn more about differentiation.
- Basic differentiation of y = x^n
- Differentiation of polynomials
- Equation of a tangent
- Equation of a normal
- General differentiation of x^n
- Second derivative
- Differentiation of tangents
- Differentiating products and quotients
- Differentiation and rates of change
- The Chain Rule
- The Product Rule
- The Quotient Rule
- Applications of differentiation 1 (displacement / velocity / acceleration)
- Applications of differentiation 2 (voltage / current)
- Differentiation and turning points
- Maximum volume of box
- Differentiation and matching graphs
END OF COURSE ASSESSMENT
Strand 5 Ordinary Level Functions and Calculus Assessment
You must score 80% or more to pass this assessment.
- Strand 5 Ordinary Level Functions and Calculus Assessment
Resource: Examination Material Archive View Resource